Dielectric spectroscopy can be used for analyzing rock electrical properties in a wide-range of frequencies. There are mainly three features in a rock system that are used for understanding the dielectric spectroscopy response: the rock solid polarization, fluid polarization, and rock-fluids interaction in the polarization process. However the relationship of these three features is non-linear and still open to research. A commercial multifrequency dielectric scanning service such as performed using Sclumberger's Dielectric Scanner tool can measure the combined rock dielectric spectroscopy response, i.e. dielectric permittivity and the rock formation conductivity at various frequencies. From these physical parameters, reservoir properties such as cementation factor, water saturation and water conductivity, formation shaliness can be estimated by the way of a dielectric mixing law. As the dielectric permittivity values of the rock solid and the fluids are separately entered in the mixing law, preferably they all should be accurately known in order to reliably estimate the reservoir properties.
Wireline logging tools can provide useful compositional data. For example, a gamma ray tool such as Schlumberger's Elemental Capture Spectroscopy (ECS) tool can be used to detect a number of elements that are in high gamma ray detection sensitivity and/or high abundance using gamma ray measurement. However, while a gamma ray logging tool such as an ECS tool can typically detect about 5-7 elements, a typical carbonate reservoir rock may have in excess of 50 elements. In the case where one or more of the compositional elements that are not detected by the gamma ray logging tool turn out to have a relatively high dielectric constant and in certain type of formation in relatively higher abundance, the effect of those elements on rock solid dielectric permittivity has never been published.
It is known that rock dielectric constant can be derived using the polarizabitility of elements within the compound. For example, R. D. Shannon, Dielectric Polarizabilities of Ions in Oxides and Fluorides, J. Appl. Physics. 73 (1), January 1993 (hereinafter “Shannon 1993”) points out that: “Good agreement between calculated and observed polarizabilities implies that additivity rules employing a sufficiently large set of dielectric oxide polarizabilities or dielectric ion polarizabilities should be useful in predicting dielectric constants of new materials and compounds whose dielectric constant has not been measured.” Shannon 1993 discusses derivation of 129 oxides and 25 fluorides polarizabilities using a least squares refinement technique in conjunction with the Clausius-Mosotti equation. Shannon 1993 also teaches that the polarizabilities can be used to estimate mean dielectric constants of “well-behaved” compounds. The frequency used in Shannon 1993 is 1 KHz to 10 MHz. M. D. Benadda, J. C. Carru, J. P. Amoureux, M. Castelain and A. Chapoton, Experiemental and Theoretical Study of the Dielectric Properties of 1-cyanoadamantane; Spectrum of the Compact Crystal from Measurements on Powder, J. Phys. D: Appl. Phys., 15 pp. 1477-1489, 1982 study the dielectric properties of 1-cyanoadamantane powder in 1 KHz to 1 GHz range. Various mixture equations have been calculated and Bottcher equation for high volume fractions (powder concentration greater than 75%) and Looyenga equation for low volume fractions (powder concentration less than 35%) seem to agree well with the experimental data. P. S. Neelakantaswamy, B. V. R. Chowdari and A. Rajaratnam, Estimation of Permittivity of a Compact Crystal by Dielectric Measurements on its Powder: A Stochastic Mixture Model for the Powder-Dielectric, J. Phys. D: Appl. Phys., 16 pp. 1785-1779, 1983 propose a stochastic mixture model to evaluate powder dielectric constant when it is embedded in a medium either air or a non-polar substance. This model is a polynomial form of combination between two medium and supposed to be working for both high and low volume fractions. 1-cyanoadamantane powder has been measured in the same frequency range as Benadda et al and agrees with the model prediction. D. A. Robinson, Calculation of the Dielectric Properties of Temperate and Tropical Soil Minerals from Ion Polarizabilites using the Clausius-Mosotti Equation, Soil Sci. Soc. Am. J. 68 pp. 1780-1785, 2004 estimates some soil mineral dielectric constants based on Clausius-Mosotti model for atomic polarizability. Predicated values agree well with measurements on single crystals that were found in the literature (within 10% accuracy).
However, most of the literature focuses on single lithology or oxides permittivity prediction. Although most of earth crusts are composed of oxides, there are oxidization deposition environment where oxygen is rich in the formation during deposition and reduction deposition where formation is undergoing chemical changes without oxygen. In this case, whether the polarizability model mentioned above can be used to describe downhole formation, especially carbonates, is subject to discussion. For carbonates with complex lithology, the documented permittivity is in the vague range of 6.1-9.1. With the application of dielectric spectroscopy in oil industry, an accurate prediction of carbonate solid permittivity with its chemical and mineral composition becomes more and more important to petrophysical interpretations.